Bifurcation Behaviour and Control on Chaotic Convection of Nanofluids with Fractional-Orders

摘要

In this paper, we study the effect of the fractional-order chaotic behaviour of nanofluids on in a fluid layer heated from below. Adams-Bashforth-Moulton predictor-corrector method was adopted to solve the fractional nonlinear system. The synchronization based on the active control theory and Lyapunov stability theory and the effective chaotic range of the fractional-order chaotic system for variation of the single control parameter have been determined. The transition to chaos occurs by a subcritical Hopf bifurcation in this fractional-order system. The results show that inhibition of chaotic convection with fractional-order can be observed when using nanofluids. Numerical simulations are provided to illustrate the effectiveness of the synchronization results derived in this paper.